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In a previous paper we investigate a Lagrangian field theory for thegravitational field (which is there represented by a section g^a of theorthonormal coframe bundle over Minkowski spacetime. Such theory, underappropriate conditions, has been proved to be equivalent to a Lorentzianspacetime structure, where the metric tensor satisfies Einstein fieldequations. Here, we first recall that according to quantum field theory ideasgravitation is described by a Lagrangian theory of a possible massive gravitonfield (generated by matter fields and coupling also to itself) living inMinkowski spacetime. The graviton field is moreover supposed to be representedby a symmetric tensor field h carrying the representations of spin two and zeroof the Lorentz group. Such a field, then (as it is well known), mustnecessarily satisfy the gauge condition given by Eq.(3) below. Next, weintroduce an ansatz relating h to the 1-form fields g^a. Then, using theClifford bundle formalism we derive, from our Lagrangian theory, the exact waveequation for the graviton and investigate the role of the gauge condition givenby Eq.(3) in obtaining a reliable conservation law for the energy-momentumtensor of the gravitational plus the matter fields in Minkowski spacetime.Finally we ask the question: does Eq.(3) fix any gauge condition for the fieldg of the effective Lorentzian spacetime structure that represents the field hin our theory? We show that no gauge condition is fixed a priory, as is thecase in General Relativity. Moreover we investigate under which conditions wemay fix Logunov gauge condition.

Gauge Fixing in the Maxwell Like Gravitational Theory in Minkowski Spacetime and in the Equivalent Lorentzian Spacetime